Part of: Synthesis digital library of engineering and computer science.

Title from PDF t.p. (viewed on October 13, 2008).

Series from website.

Includes bibliographical references.

Partial differential equations in engineering -- Introductory comments -- Fundamental concepts -- Problems -- The heat conduction (or diffusion) equation -- Rectangular Cartesian coordinates -- Cylindrical coordinates -- Spherical coordinates -- The Laplacian operator -- Boundary conditions -- The vibrating string -- Boundary conditions -- Vibrating membrane -- Longitudinal displacements of an elastic bar -- Further reading -- The Fourier method: Separation of variables -- Heat conduction -- Scales and dimensionless variables -- Separation of variables -- Superposition -- Orthogonality -- Lessons -- Problems -- Scales and dimensionless variables -- Separation of variables -- Choosing the sign of the separation constant -- Superposition -- Orthogonality -- Lessons -- Scales and dimensionless variables -- Getting to one nonhomogeneous condition -- Separation of variables -- Choosing the sign of the separation constant -- Superposition -- Orthogonality -- Lessons -- Scales and dimensionless variables -- Relocating the nonhomogeneity -- Separating variables -- Superposition -- Orthogonality -- Lessons -- Problems -- Vibrations -- Scales and dimensionless variables -- Separation of variables -- Orthogonality -- Lessons -- Problems -- Further reading -- Orthogonal sets of functions -- Vectors -- Orthogonality of vectors -- Orthonormal sets of vectors -- Functions -- Orthonormal sets of functions and Fourier series -- Best approximation -- Convergence of Fourier series -- Examples of Fourier series -- Problems -- Sturm-Liouville problems: Orthogonal functions -- Orthogonality of Eigenfunctions -- Problems -- Further reading -- Series solutions of ordinary differential equations -- General series solutions -- Definitions -- Ordinary points and series solutions -- Lessons: Finding series solutions for differential equations with ordinary points -- Problems -- Regular singular points and the method of Frobenius -- Lessons: Finding series solution for differential equations with regular singular points -- Logarithms and second solutions -- Problems -- Bessel functions -- Solutions of Bessel's equation -- Here are the rules -- Fourier-Bessel series -- Problems -- Legendre functions -- Associated Legendre functions -- Problems -- Further reading -- Solutions using Fourier series and integrals -- Conduction (or diffusion) problems -- Time-dependent boundary conditions -- Vibrations problems -- Problems -- Fourier integrals -- Problem -- Further reading -- Integral transforms: The Laplace transform -- The Laplace transform -- Some important transforms -- Exponentials -- Shifting in the S-domain -- Shifting in the time domain -- Sine and cosine -- Hyperbolic functions -- Powers of t: tm -- Heaviside step -- The Dirac delta function -- Transforms of derivatives -- Laplace transforms of integrals -- Derivatives of transforms -- Linear ordinary differential equations with constant coefficients -- Some important theorems -- Initial value theorem -- Final value theorem -- Convolution -- Partial fractions -- Nonrepeating roots -- Repeated roots -- Quadratic factors: Complex roots -- Problems -- Further reading -- Complex variables and the Laplace inversion integral -- Basic properties -- Limits and differentiation of complex variables analytic functions -- Integrals -- The Cauchy integral formula -- Problems -- Solutions with Laplace transforms -- Mechanical vibrations -- Problems -- Diffusion or conduction problems -- Problems -- Duhamel's theorem -- Problems -- Further reading -- Sturm-Liouville Transforms -- A Preliminary Example: Fourier Sine Transform -- Generalization: The Sturm-Liouville Transform: Theory -- The Inverse Transform -- Problems -- Further Reading -- Introduction to Perturbation methods -- Examples from algebra -- Regular perturbation -- Singular perturbation -- Appendix A: The roots of certain transcendental equations.